Hidden-order phases that occur in a number of correlated f -electron systems are among the most elusive states of electronic matter. Their investigations are hindered by the insensitivity of standard physical probes, such as neutron diffraction, to the order parameter that is usually associated with higher-order multipoles of the f orbitals. The heavy-fermion compound Ce₃Pd₂₀Si₆ exhibits magnetically hidden order at subkelvin temperatures, known as phase II. Additionally, for magnetic field applied along the [001] cubic axis, another phase II′ was detected, but the nature of the transition from phase II to phase II′ remained unclear. Here we use inelastic neutron scattering to argue that this transition is most likely associated with a change in the propagation vector of the antiferroquadrupolar order from (111) to (100). Despite the absence of magnetic Bragg scattering in phase II′ , its ordering vector is revealed by the location of an intense magnetic soft mode at the (100) wave vector, that is orthogonal to the applied field. At the II- II′ transition, this mode softens and transforms into quasielastic and nearly Q-independent incoherent scattering, which is likely related to the non-Fermi-liquid behavior recently observed at this transition. Our experiment also reveals sharp collective excitations in the field-polarized paramagnetic phase, after phase II′ is suppressed in fields above 4T.